Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping

TL;DR

This paper tackles the challenge of learning signed distance functions (SDFs) from noisy point clouds without ground-truth distances, normals, or clean data. It proposes a noise-to-noise learning paradigm built around a denoising function $F$, an $SDF$ predictor $f_{m{ heta}}$, and a geometric-consistency regularizer, with $L_{EMD}$ driving robust statistical reasoning across unordered observations. A fast learning variant using multi-resolution hash encodings (Inspired by Instant-NGP) accelerates training to about one minute and includes $L_{pull}$ and $L_{reg}$ to stabilize far-field regions. The authors further show how to extract an SDF prior from noisy SfM points to guide multi-view reconstruction with NeuS, improving artifact suppression and convergence. Across diverse datasets (shapes and scenes) and tasks (denoising, upsampling, surface reconstruction, and multi-view reconstruction), the method achieves state-of-the-art performance while significantly reducing training time, highlighting its practical impact for robust 3D surface reconstruction from real-world noisy data.

Abstract

Learning signed distance functions (SDFs) from point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs from noisy point clouds. To overcome this challenge, we propose to learn SDFs via a noise to noise mapping, which does not require any clean point cloud or ground truth supervision. Our novelty lies in the noise to noise mapping which can infer a highly accurate SDF of a single object or scene from its multiple or even single noisy observations. We achieve this by a novel loss which enables statistical reasoning on point clouds and maintains geometric consistency although point clouds are irregular, unordered and have no point correspondence among noisy observations. To accelerate training, we use multi-resolution hash encodings implemented in CUDA in our framework, which reduces our training time by a factor of ten, achieving convergence within one minute. We further introduce a novel schema to improve multi-view reconstruction by estimating SDFs as a prior. Our evaluations under widely-used benchmarks demonstrate our superiority over the state-of-the-art methods in surface reconstruction from point clouds or multi-view images, point cloud denoising and upsampling.

Figures (35)

• Figure 1: We introduce to learn signed distance functions (SDFs) for single noisy point clouds. Our method does not require ground truth signed distances, point normals or clean points as supervision for training. We achieve this via learning a mapping from one noisy observation to another or even on a single observation. Our novel learning manner is supported by modern Lidar systems which capture 10 to 30 noisy observations per second. We show the SDF learned from (a) a single real scan containing $10M$ points, (b) the denoised point cloud and (c) the reconstructed surface. Fig. \ref{['fig:Paris']} demonstrates our superiority over the latest surface reconstructions in this case.
• Figure 2: Given corrupted observations captured by a Lidar system per second, we learn a SDF without supervision or normals.
• Figure 3: (a) Multiple paths (arrows) to pull a noise (green point) onto surface (dashed curve) but only one is the shortest (green arrows). (b) The incorrect paths (black arrows) to pull noises onto surface. (c) The expected paths (green arrows) to pull noises to points (blue square) on surface. (d) The effect of Geometric Consistency (GC).
• Figure 4: The comparison with CD and EMD as the distance metric $L$ from in (b) to (e). The effect of geometric regularization in (f) and (g). (a) is noisy point cloud, (h) is the ground truth.
• Figure 5: (a) Visualization of optimization in $4$ epochs via noise to noise mapping. $3$ queries (black cubes) sampled from one noisy point cloud get pulled onto the surface. For each query, we minimize its distance to all targets (in the same color) matched from another noisy point cloud by the mapping $\phi$ in metric $L$. More details can be found in our video at the project page. (b) Surface reconstruction and multiple level-sets.